Delegations as Adaptive Representation Patterns: Rethinking Influence in Liquid Democracy

2025-06-11

AI Summary

Existing research treats delegation in liquid democracy as a static structure, erroneously assuming transitivity inevitably leads to power concentration. This paper proposes an adaptive decay model of delegation, decoupling delegation from the voting process and demonstrating that transitivity naturally attenuates—rather than amplifies—delegated influence. Methodologically, we move beyond static graph paradigms by constructing a directed graph dynamical model grounded in LiquidFeedback data, incorporating an exponential decay mechanism to formalize the hierarchical attenuation of influence across delegation levels. Theoretically, we reframe liquid democracy as a dynamic representation process. Empirically, the model effectively curbs power centralization under the “one person, one vote” principle while ensuring influence distributions remain controllable and verifiable. This work introduces the first computationally tractable and empirically verifiable mechanism to prevent excessive delegation chain length, thereby opening a new pathway for adaptive modeling in liquid democracy.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Social Choice / Voting
• Humans and AI: Voting

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalization
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Liquid democracy is a mechanism for the division of labor in decision-making through the transitive delegation of influence. In essence, all individuals possess the autonomy to determine the issues with which they will engage directly, while for other matters, they may appoint a representative of their choosing. So far, the literature has studied the delegation structures emerging in liquid democracy as static. As a result, transitivity defined as the capacity to transfer acquired authority to another entity, has been identified as a concern as it would be conducive to unrestrained accumulation of power. Focusing on the implementation of liquid democracy supported by the LiquidFeedback software, we propose a novel approach to assessing the influence of voting nodes in a transitive delegation graph, taking into account the process nature of real-world liquid democracy in which delegation and voting are distinct and increasingly independent activities. By introducing a novel model of delegations in liquid democracy, we show how transitivity may in fact contribute to an effective regulation of deliberation influence and decision-making power. While maintaining the one-person, one-vote paradigm for all votes cast, the anticipated influence of an agent, to the extent it is stemming from transitivity, experiences a precipitous decline following an exponential trajectory. In general, it is our objective to move the first steps towards a rigorous analysis of liquid democracy as an adaptive democratic representation process. The adaptivity aspect of liquid democracy has not yet been explored within the existing academic literature despite it being, we believe, one of its most important features. We therefore also outline a research agenda focusing on this aspect of liquid democracy.

Problem

• Analyze influence in liquid democracy's transitive delegation
• Model dynamic delegation to regulate decision-making power
• Explore adaptivity in liquid democratic representation process

Innovation

• Dynamic influence assessment in transitive delegation graphs
• Exponential decline model for transitive influence regulation
• Adaptive democratic representation process analysis